## Valentin Goranko

Department of Mathematics

Rand Afrikaans University

PO Box 524

Auckland Park 2006

Johannesburg

South Africa

vfg@na.rau.ac.za

http://www.rau.ac.za/staff/goranko_vf

### Abstract

We study a generic problem of proving semantic completeness of a logical system with respect to a class of ``standard models'', provided a weaker completeness result with respect to a larger class of ``general models'' has been obtained. We propose a natural topological approach to this problem based on the notion of * logical topology * and the related concept of * logical approximation. *We then obtain some general results regarding these concepts and then discuss them in the framework of first-order logic. The paper ends with an example of a particualr application of the ideas developed here, and a discussion on further research.

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